A126964 a(n) = 2*n*(6*n-1).

0, 10, 44, 102, 184, 290, 420, 574, 752, 954, 1180, 1430, 1704, 2002, 2324, 2670, 3040, 3434, 3852, 4294, 4760, 5250, 5764, 6302, 6864, 7450, 8060, 8694, 9352, 10034, 10740, 11470, 12224, 13002, 13804, 14630, 15480, 16354, 17252, 18174, 19120, 20090, 21084

Offset: 0

Author

N. J. A. Sloane, Mar 21 2007

Keywords

• nonn
• easy

References

• V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

GAP

List([0..50], n-> 2*Binomial(6*n,2)/3 ); # G. C. Greubel, Jan 29 2020

Magma

[2*n*(6*n-1) : n in [0..50]]; // Wesley Ivan Hurt, Dec 03 2016

Maple

A126964:=n->2*n*(6*n-1): seq(A126964(n), n=0..60); # Wesley Ivan Hurt, Dec 03 2016

Mathematica

Table[2n(6n-1),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,44},50] (* Harvey P. Dale, Nov 19 2011 *)

PARI

a(n)=2*n*(6*n-1) \\ Charles R Greathouse IV, Jun 16 2017

Sage

[2*binomial(6*n,2)/3 for n in (0..50)] # G. C. Greubel, Jan 29 2020

Formula

a(n) = 24*n + a(n-1) - 14 for n>0, a(0)=0. - Vincenzo Librandi, Nov 23 2010

From Harvey P. Dale, Nov 19 2011: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=10, a(2)=44.

G.f.: (10*x + 14*x^2)/(1 - x)^3. (End)

From Ilya Gutkovskiy, Dec 04 2016: (Start)

Sum_{n>=1} 1/a(n) = (4*log(2) + 3*log(3) - sqrt(3)*Pi)/4 = 0.15675687388...

E.g.f.: 2*x*(5 + 6*x)*exp(x). (End)

a(n) = Sum_{i=n..5*n-1} i. - Wesley Ivan Hurt, Dec 04 2016